Though he added that he would welcome a third-party investigation.
Between 1999 and 2015, hundreds of sub-postmasters and postmistresses were wrongly prosecuted after Horizon made it look like money was missing from their branches.
Fujitsu’s Horizon contract is up for renewal early next year and could be extended for a further five years.
Patterson said he was “very worried” about what might happen if this happens because of how unreliable Horizon is.
“In my experience… if you don’t keep [IT systems] upgraded, I cannot determine what will or will not happen, which is part of my nervousness of it being extended,” he said.
Monday marked the start of the final week of evidence at the inquiry, more than two and a half years since it started hearing evidence in public.
Mr Patterson said Fujitsu was committed to paying out compensation to the victims of the scandal, calling it a “moral obligation”, but said the firm was waiting until the end of the inquiry before actually doing so.
In a heated exchange with Sam Stein KC, who represented some of the victims, Mr Patterson was pushed on why this was.
“You already accept that there is a need for Fujitsu to put its money where its mouth is,” said Mr Stein.
Mr Patterson said the company wanted to hear all the evidence before going ahead. “These are complex matters and we need to understand all the components,” he said.
Earlier in the day, Conservative Party leader Kemi Badenoch gave evidence – as the former business secretary, the government-owned Post Office came under her remit.